Question

A sphere is inscribed in a cylinder such that sphere touches the cylinder. Show that the curved surface of sphere is equal to the curved surface area of cylinder.

Answer 1

Curved surface area of sphere = Curved surface area of cylinder.

1) Curved surface area of a sphere.

CSA of sphere = 4πr²

2) Curved surface area of a cylinder.

CSA of cylinder = 2πrh

But h = 2r, so

CSA of cylinder = 2πr(2r) = 4πr²

CSA of sphere = 4πr2 = CSA of cylinder

Hence proved.